Find the Determinant [[2k-mx^2,-k],[-k,k-m/2*x^2]]

Problem

det(2*k−m*x2)

Solution

1. Identify the formula for the determinant of a 2×2 matrix [[a,b],[c,d]] which is a*d−b*c

2. Substitute the elements of the matrix into the formula.

a=2*k−m*x2

b=−k

c=−k

d=k−m/2*x2

3. Set up the product calculation.

det(=)*(2*k−m*x2)*(k−m/2*x2)−(−k)*(−k)

4. Expand the first term using the FOIL method.

(2*k)*(k)+(2*k)*(−m/2*x2)+(−m*x2)*(k)+(−m*x2)*(−m/2*x2)

2*k2−m*k*x2−m*k*x2+(m2)/2*x4

5. Simplify the expanded expression by combining like terms.

2*k2−2*m*k*x2+(m2)/2*x4

6. Subtract the product of the off-diagonal elements b*c=(−k)*(−k)=k2

2*k2−2*m*k*x2+(m2)/2*x4−k2

7. Combine the remaining like terms to find the final expression.

k2−2*m*k*x2+(m2)/2*x4

Final Answer

det(2*k−m*x2)=(m2)/2*x4−2*m*k*x2+k2

Want more problems? Check here!